View source for PARADISCYL:Cylinder-Benchmark2

=Benchmarks to check traction boundary condition on the surface=
==ILL RYU==
===May 1, 2010===

From these benchmarks, we like to confirm if the zero traction boundary condition is satisfird on the surface, which means that the traction force should be zero on the cylinder boundary. To do that, two models are prepared , varying the geometry of dislocation loop, as following figures.

== Model geometries==
<gallery caption="Slip system" widths="400px" heights="400px" perrow="2">
Image:Cylinder_loop_flat.png  |[Slip system in the flat loop]	
Image:Cylinder_loop_inclinded.png |[Slip system in the inclined loop ]	
</gallery>

<gallery widths="400px" heights="400px" perrow="2">
Image:Cylinder_loop_flat.jpg  |[flat loop]	
Image:Cylinder_loop_inclined.jpg |[Inclined loop ]	
</gallery>

To satisfy traction zero boundary, we need to check if <math>\sigma_{rr}\,\!</math> ,<math>\sigma_{r \theta}\,\!</math>, and
<math>\sigma_{rz}\,\!</math> can be zero on the surface. 
----

== Total stress on the cylinder surface==
<gallery caption="Flat loop" widths="900px" heights="500px" >
Image:Tot_flat.jpg‎  
</gallery>
<gallery caption="Inclinded loop" widths="900px" heights="500px" >
Image:Tot_inclined.jpg‎  
</gallery>

== Conclusion ==
From the plot, we can see that <math>\sigma_{rr}\,\!</math> ,<math>\sigma_{r \theta}\,\!</math>, and <math>\sigma_{rz}\,\!</math> are zero on the surface.Therefore, the traction boundary condition is satisfied well.  

=== Input & plot files  ===
[[Media: Cylinder_loop.tar‎  | ParaDiS input ]] <br>
[[Media: Plot_stress.tar| Matlab file for plot ]] <br>